Faster algorithm for computing the edit distance between SLP-Compressed strings

Authors:
Paweł Gawrychowski
Affiliations:
Institute of Computer Science, University of Wrocław, Poland,Max-Planck-Institute für Informatik, Saarbrücken, Germany
Venue:
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
Year:
2012

Citing 5
Cited 0

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Fast distance multiplication of unit-Monge matrices

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Polylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity

FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
The smallest grammar problem

IEEE Transactions on Information Theory
Processing compressed texts: a tractability border

CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching

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Abstract

Given two strings described by SLPs of total size n, we show how to compute their edit distance in $\mathcal{O}(nN\sqrt{\log\frac{N}{n}})$ time, where N is the sum of the strings length. The result can be generalized to any rational scoring function, hence we improve the existing $\mathcal{O}(nN\log N)$ [10] and $\mathcal{O}(nN\log\frac{N}{n})$ [4] time solutions. This gets us even closer to the $\mathcal{O}(nN)$ complexity conjectured by Lifshits [7]. The basic tool in our solution is a linear time procedure for computing the max-product of a vector and a unit-Monge matrix, which might be of independent interest.